How many of each type of sandwich should the family make if the goal is to use up all of the buns, patties, and cheese slices?

Question

a plain hamburger requires one ground beef patty and a bun. A cheeseburger requires one ground beef patty, one slice of cheese, and a bun. A double cheeseburger requires two ground beef patties, two slices of cheese, and a bun. Frozen hamburger patties are typically sold in packs of 12; hamburger buns, in packs of 8; and cheese slices, in packs of 24. A family is in charge of providing burgers for a neighborhood block party. It has purchased 13 packs of buns, 11 packs of hamburger patties, and 3 packs of cheese slices.

Answer 1

Hi Camille.

 

That is a lot of information!!!

 

The first thing I would do is figure out how many total buns you have, how many total patties you have, and how many slices of cheese you have.   This would look like:

 

13 packs of buns * 8 buns/pack = 104 buns to use

11 packs of patties * 12 patties/pack = 132 beef patties to use

3 packs of cheese slices * 24 slices/pack = 72 slices of cheese to use.

 

Now, assign variables to plain hamburgers (H), cheeseburgers (C), and double cheeseburgers (D).

 

Set up 3 equations based on the number of ingredients needed for each item

 

So:   

 

H + C + D = 104   

(this is the number of buns per item; have to total 104 because that is how many buns we need to use up.)

 

H + C + 2D = 132 

(this is the number of patties per item;  have to total 132 because that is how many buns we need to use up.)

 

0H + C + 2D = 72

(this is the number of cheese slices per item;  have to total 72 because that is how many cheese slices we need to use up).

 

So there is your system of 3 equations and 3 unknowns.  I do not know how your teacher wants you to solve it...  You can use substitution, elimination, matrices...   Or a calculator (hand held or online) that can solve a system of 3 equations.

 

However you are required to solve this, I get that you should make

 

60 plain hamburgers  (H = 60)

16 cheeseburgers (C = 16)

28 double  cheeseburgers (D = 28)

 

Check to see that these work...